1. Field of the Invention
This invention relates to micro-electromechanical system (“MEMS”) devices that sense inertial rotation and acceleration, commonly referred to as gyroscopes and accelerometers. More specifically, the invention relates to MEMS resonant gyroscopes and accelerometers.
2. Related Art
Precision micro-electromechanical accelerometers and gyroscopes have wide application in the field of inertial navigation and guidance. Such sensors are manufactured using sophisticated semiconductor manufacturing, or “micromachining,” techniques, and typically incorporate at least one planar mass, typically of silicon, pendulously mounted adjacent to at least one planar structure, also typically of silicon, so as to define an electrical capacitance between the mass and structure. Movement of the mass relative to the structure in response to inertial forces imposed on the sensor, e.g., in response to an acceleration of the sensor along an “axis of sensitivity” thereof, results in a change in the capacitance that is a direct measure of the sensor's acceleration.
In addition to such “direct” measurements of linear accelerations, such sensors can also be used advantageously within an inertial system to “indirectly” measure rotational velocity, or angular rates, about an axis of sensitivity of the sensor, through use of the well known Coriolis principle. Thus, a body moving with a given velocity ν relative to a coordinate system that is rotating with an angular velocity {dot over (θ)} will experience a Coriolis acceleration α that is equal to the vector cross-product 2{dot over (θ)}X ν, which is directed normal to the path of rotation of the body, and which acts to deflect the relative velocity ν of the body in the direction of the angular velocity {dot over (θ)} of the system. Hence, if a rotational relative velocity, or more practically for the planar types of structures found in MEMS gyroscopes, a vibratory, sinusoidally varying relative velocity ν=V sin ωt, i.e., “dither”, is imparted to the mass of the sensor, then the capacitance between the mass and the adjacent structure will likewise vary sinusoidally in response thereto. If an angular velocity {dot over (θ)} is then imparted to the sensor, it will experience a Coriolis acceleration given by the relationship α=2{dot over (θ)}X V sin ωt, in which the Coriolis acceleration α may be seen as the modulation of the sinusoidally varying capacitance signal of the sensor with a signal that is a function of the angular rotation {dot over (θ)} of the sensor, and from which the desired angular rate {dot over (θ)} of the sensor may therefore be extracted using well known demodulation techniques.
Examples of such prior art MEMS inertial sensors and “microgyroscopes” may be found in the patent literature, e.g., in U.S. Pat. Nos. 6,758,093 to T. K. Tang et al.; 6,675,630 to A. D. Challoner et al.; 6,651,500 to R. E. Stewart et al.; 6,595,056 to R. E. Stewart; 6,539,801 to R. C. Gutierrez et al.; 6,487,907 to T. K. Tang et al.; 6,367,786 to R. C. Gutierrez et al.; 6,360,601 to A. D. Challoner et al.; and, 5,894,090 to T. K. Tang et al.
One measure of the accuracy of a MEMS inertial sensor is the stability over time of the capacitance between the moving masses and fixed structures, i.e., its “bias stability.” Prior art MEMS resonant gyroscopes designed to achieve a bias stability of at least 10 degrees per hour typically use symmetrical resonating structures, such as rings. In a symmetrical resonating structure, there are two “nearly degenerate” modes that couple very efficiently in response to inertial rotation. However, due to the small sensing area available for capacitive sensing, MEMS gyroscopes that use ring structures typically exhibit high angle random walk, or rotation-rate white noise. In addition, due to the crystalline structure of silicon, there is a dependence of spring constant with orientation. This breaks the symmetry of the structure and adversely affects the drift performance of MEMS gyroscopes that use ring structures. Some of the limitations of ring structures have been overcome by using other structural shapes, such as a “cloverleaf” gyroscope with an underlying post. However, these devices are not substantially planar in configuration, and consequently, are more difficult to manufacture and package.
Additionally, for any symmetrical structure, the resonant motion of the structure about its axis of symmetry can be described as a linear combination of two orthogonal modes of rotation or oscillation. The resonant motions involve resilient flexing by different portions of the structure. As a practical matter, the symmetry of a symmetrical structure can never be really perfect, and accordingly, to achieve an accurate sensor, expensive, high-precision machining of the structure is required to approach true symmetry as closely as possible.
Accordingly, there is a long-felt but as yet unsatisfied need in the industry for a highly accurate, substantially planar MEMS resonant gyroscope that is simple in construction, avoids expensive, high-precision machining, and is therefore easy and inexpensive to manufacture and assemble.